GCD GCD / HCF Calculator

GCD / HCF Result

What is GCD / HCF?

The Greatest Common Divisor (GCD), also known as Highest Common Factor (HCF), is the largest number that divides two or more integers without leaving a remainder.

GCD(48, 18) = 6
Because 6 is the largest number that divides both 48 and 18 evenly.

Euclidean Algorithm

The most efficient method to find GCD uses the Euclidean algorithm:

  1. Divide the larger number by the smaller number.
  2. Replace the larger number with the remainder.
  3. Repeat until remainder is 0.
  4. The last non-zero remainder is the GCD.
GCD(48, 18): 48 = 18×2 + 12 → 18 = 12×1 + 6 → 12 = 6×2 + 0 → GCD = 6

Frequently Asked Questions

What is the GCD of 12 and 18? ▼
GCD(12, 18) = 6. The common factors of 12 and 18 are 1, 2, 3, and 6. The greatest is 6.
What is the difference between GCD and HCF? ▼
GCD (Greatest Common Divisor) and HCF (Highest Common Factor) are different names for the exact same concept. They are identical.
What is GCD used for? ▼
GCD is used to simplify fractions (divide both numerator and denominator by GCD), find LCM, solve linear Diophantine equations, and in cryptography algorithms like RSA.